Abstract
This article studies the blowup time of weak solutions to the degenerate parabolic equation \(u_{t}-\Delta _{p}u=\lambda u^{m}+\mu |\nabla u|^{q}\) with homogeneous Dirichlet boundary condition in a bounded smooth domain. We first obtain an upper bound and a lower one for the blowup time of \(L^{\infty }\) blowup solutions and then get the upper bound for the blowup time of gradient blowup solutions.
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Acknowledgements
We appreciate Professor Bei Hu for his valuable suggestions, and we would like to express our sincere gratitude to the anonymous referees for their very careful readings of the paper and for all their corrections, insightful comments and helpful suggestions.
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This work was supported by the National Natural Science Foundation of China (Nos. 11371286, 11401458) and the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2019JM-165).
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Lu, H., Zhang, Z. Blowup time estimates for a parabolic p-Laplacian equation with nonlinear gradient terms. Z. Angew. Math. Phys. 70, 90 (2019). https://doi.org/10.1007/s00033-019-1133-z
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DOI: https://doi.org/10.1007/s00033-019-1133-z